I realize that this is purely anecdotal, but may answer your question.
My father got me playing around with programming when I was very young -- I think six or eight years old. Some of my first memories involve our VIC-20 computer.
While a lot of what I did was just typing in simple programs from a book, I did some experimentation on my own, and it became pretty obvious how variables, loops, and the rest worked.
When I hit school I was mathematically so far ahead of everybody else, not because I'm some kind of genius, but because I had already spent a lot of time unknowingly learning algebra.
This was a disadvantage, because the school system wasn't built to cope with a kid that understood algebra before he had memorized the multiplication table.
As an adult, however, I've enjoyed a pretty serious advantage when it comes to understanding abstract concepts, especially anything involving symbolic manipulation, and I think I can thank that VIC-20 BASIC manual from many years ago for it.
I wouldn't be too worried about starting a kid out 'too soon', provided that other areas of the child's mental development aren't neglected in favor of developing mathematical skills.
I had a similar experience. My father and grandfather introduced me to computers and programming at a very young age, and I ultimately taught myself algebra, geometry, and basic trigonometry by age 10.
From fifth grade, I was bored out of my mind during math class. In sixth grade, my math teacher recognized my boredom to be a lack of challenge and decided she should do something about it. I was pulled into the vice principal's office at one point and asked to slow down my at-home learning because the teachers did not know what to do with me during class.
Eventually, we settled on a solution: I became the equivalent of a teacher's aid for my middle school class and tutored other kids who were having difficulty. This instilled a love for teaching that I carry with me to this day.
I don't think we should discourage children from learning at a fast pace as long as they appear to retain the information and it doesn't compromise other aspects of development. On the contrary, we need to find a way to help our education system cope with children learning things outside the classroom.
My father got me playing around with programming when I was very young -- I think six or eight years old. Some of my first memories involve our VIC-20 computer.
While a lot of what I did was just typing in simple programs from a book, I did some experimentation on my own, and it became pretty obvious how variables, loops, and the rest worked.
When I hit school I was mathematically so far ahead of everybody else, not because I'm some kind of genius, but because I had already spent a lot of time unknowingly learning algebra.
This was a disadvantage, because the school system wasn't built to cope with a kid that understood algebra before he had memorized the multiplication table.
As an adult, however, I've enjoyed a pretty serious advantage when it comes to understanding abstract concepts, especially anything involving symbolic manipulation, and I think I can thank that VIC-20 BASIC manual from many years ago for it.
I wouldn't be too worried about starting a kid out 'too soon', provided that other areas of the child's mental development aren't neglected in favor of developing mathematical skills.